29edo: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 212999628 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213002142 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-22 19: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-22 19:14:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213002142</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= | |||
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. | 29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. | ||
| Line 14: | Line 16: | ||
The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. | The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. | ||
=Intervals= | |||
|| Degrees of 29-EDO || Cents value || | || Degrees of 29-EDO || Cents value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
| Line 44: | Line 46: | ||
|| 26 || 1075.862 || | || 26 || 1075.862 || | ||
|| 27 || 1117.241 || | || 27 || 1117.241 || | ||
|| 28 || 1158.621 ||</pre></div> | || 28 || 1158.621 || | ||
=Music= | |||
[[http://tinyurl.com/45lancy|Paint in the Water 29]] by [[Igliashon Jones]]</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>29edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>29edo</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
<!-- ws:end:WikiTextTocRule:10 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1> | |||
<br /> | <br /> | ||
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | 29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | ||
| Line 54: | Line 61: | ||
The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing.<br /> | The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
| Line 240: | Line 247: | ||
</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1> | |||
<a class="wiki_link_ext" href="http://tinyurl.com/45lancy" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a></body></html></pre></div> | |||
Revision as of 19:14, 22 March 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-03-22 19:14:56 UTC.
- The original revision id was 213002142.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc|flat]] =<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= 29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. 29 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[positive temperament]] -- a Superpythagorean instead of a Meantone system. The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. =Intervals= || Degrees of 29-EDO || Cents value || || 0 || 0 || || 1 || 41.379 || || 2 || 82.759 || || 3 || 124.138 || || 4 || 165.517 || || 5 || 206.897 || || 6 || 248.276 || || 7 || 289.655 || || 8 || 331.034 || || 9 || 372.414 || || 10 || 413.793 || || 11 || 455.172 || || 12 || 496.552 || || 13 || 537.931 || || 14 || 579.310 || || 15 || 620.690 || || 16 || 662.069 || || 17 || 703.448 || || 18 || 744.828 || || 19 || 786.207 || || 20 || 827.586 || || 21 || 868.966 || || 22 || 910.345 || || 23 || 951.724 || || 24 || 993.103 || || 25 || 1034.483 || || 26 || 1075.862 || || 27 || 1117.241 || || 28 || 1158.621 || =Music= [[http://tinyurl.com/45lancy|Paint in the Water 29]] by [[Igliashon Jones]]
Original HTML content:
<html><head><title>29edo</title></head><body><!-- ws:start:WikiTextTocRule:6:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
<!-- ws:end:WikiTextTocRule:10 --><br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1>
<br />
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br />
<br />
29 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a <a class="wiki_link" href="/positive%20temperament">positive temperament</a> -- a Superpythagorean instead of a Meantone system. <br />
<br />
The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>Degrees of 29-EDO<br />
</td>
<td>Cents value<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>41.379<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>82.759<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>124.138<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>165.517<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>206.897<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>248.276<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>289.655<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>331.034<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>372.414<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>413.793<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>455.172<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>496.552<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>537.931<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>579.310<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>620.690<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>662.069<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>703.448<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>744.828<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>786.207<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>827.586<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>868.966<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>910.345<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>951.724<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>993.103<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1034.483<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1075.862<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1117.241<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>1158.621<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1>
<a class="wiki_link_ext" href="http://tinyurl.com/45lancy" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a></body></html>